Linear polynomial least squares

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Homework Help Overview

The discussion revolves around constructing normal equations for linear polynomial least squares to fit given data points. The subject area includes linear regression, QR decomposition, eigenvalues, and polynomial interpolation.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the formulation of normal equations and inquire about the conditions for zero eigenvalues in the context of the normal equation matrix. There are also mentions of definitions and examples as starting points for understanding.

Discussion Status

The discussion includes attempts to clarify the normal equation setup and some participants have indicated progress on part of the problem. However, there is no explicit consensus on the overall approach or solutions being pursued.

Contextual Notes

Some participants express uncertainty about the problem requirements, and there is a suggestion to refer to definitions and examples from textbooks. The nature of the homework implies constraints on providing complete solutions.

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Construct the normal equations for the linear polynomial least squares to fit the data x = [1 0 -1], y=[3;2;-1]. (a) Find the parameters of the linear regression u1, u2 using QR decomposition, and plot the data and the fit curve in a graph (paper and pencil). (b) Calculate the eigenvalues of the normal equation matrix A'*A for the above data from the characteristic polynomial. (c) Write down quadratic interpolation polynomial in Lagrange form to interpolate the three data points. (d) Assume that the normal equation matrix A'*A is generated by A with m rows and n columns, m>=n. Explain under which conditions there would be a zero eigenvalue among the eigenvalues of the matrix of the normal equations.
 
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anyone have any idea on how to do this?
 
A more important question is if you have any ideas.
 
the answer is NO, anyone else?
 
Definitions are always a good place to start. There might even be an example in your book!
 
is the normal equation At *A*u = At *b, At being A transpose?
 
ok, party 'a' done, if anyone cares
 

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